Question

A trader wants to earn 16(2/3) % after allowing a discount of 25%. Find by how much % he has to increase his cost price to make market price?

Answer 1

Hint: In this particular type of question use the concept that selling price is the difference of the market price and the discounted percentage times the market price, and percentage profit is the ratio of the difference of the selling price and the cost price to the cost price multiplied by 100, so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
Profit wants to earn by the trader = 16(2/3) %
Discount allowed by the trader = 25%.
Let the cost price of the article be Rs. x
Let the market price of the article be Rs. y
Now he gives a 25 % discount on the market price.
Now as we know that the selling price is the difference of the market price and the discounted percentage times the market price.
So the price a buyer has to pay i.e. selling price of the article = y - $\dfrac{{25}}{{100}}y$
Therefore, selling price = y – 0.25y = 0.75y
Now the profit earned by the trader = 16(2/3) % = (50/3) %
Now as we know that the percentage profit is the ratio of the difference of the selling price and the cost price to the cost price multiplied by 100.
$ \Rightarrow \dfrac{{50}}{3} = \dfrac{{0.75y - x}}{x} \times 100$
Now simplify this we have,
$ \Rightarrow \dfrac{1}{6} = \dfrac{{0.75y - x}}{x}$
$ \Rightarrow x = 4.5y - 6x$
$ \Rightarrow 7x = 4.5y$
$ \Rightarrow y = \left( {\dfrac{7}{{4.5}}} \right)x$
Now we have to find out by how much % he has to increase his cost price to make market price.
So the percentage increase is the ratio of the market price and the cost price to the cost price multiplied by 100.
So the percentage increase is = \[\dfrac{{{\text{market price - cost price}}}}{{{\text{cost price}}}} \times 100\]
So the percentage increase is = \[\dfrac{{y - x}}{x} \times 100\]
So the percentage increase is = \[\dfrac{{\dfrac{7}{{4.5}}x - x}}{x} \times 100\]
$ \Rightarrow \dfrac{{7 - 4.5}}{{4.5}} \times 100$
$ \Rightarrow \dfrac{{2.5}}{{4.5}} \times 100$
$ \Rightarrow \dfrac{5}{9} \times 100 = \dfrac{{500}}{9} = 55.55$%
So this is the required answer.

Note:Whenever we face such types of questions the key concept we have to remember is that always recall that the percentage increase is the ratio of the market price and the cost price to the cost price multiplied by 100, so first find out the market price in terms of the cost price as above calculated then substitute the values in the above described formula and simplify we will get the required answer.